Title: The Role of Orbital Angular Momentum in the Parton Distributions of a Heavy Nucleus
Abstract: The notion of a "parton distribution function" (PDF) dates back to Feynman's parton model, which explained inclusive deep inelastic scattering in terms of one-dimensional distributions of quarks and gluons inside a hadron. But this simple concept of a PDF as the expectation value of a parton density operator becomes muddied when embedded in the full field theory of QCD, and the more descriptive the PDF -- from a 1D distribution, to a 3D distribution, to a 5D distribution -- the more subtle and complex the meaning of the PDF becomes. The seemingly-simple generalization to a three-dimensional "transverse-momentum-dependent PDF" (TMD) blurs the line between the parton density and the role of initial- and final-state interactions. Particularly for observables like spin asymmetries in semi-inclusive deep inelastic scattering, physical properties like the partonic orbital angular momentum and the color-Lorentz force become entangled with subtle questions of non-universality, process dependence, and factorization breaking. These issues are among the rich features of QCD which we are now beginning to understand as we probe the internal structure of hadrons at ever-deeper levels, trying to resolve -- among many other puzzles -- the decomposition of the proton spin in terms of partonic spins and orbital angular momenta.

In tandem, we have learned from the study of QCD at high energies that when the density of partons becomes high enough, emergent degrees of freedom can greatly simplify the complex partonic dynamics. At high energies or in heavy nuclei, a resummation of the high-density effects leads to an effective theory (sometimes called the "color-glass condensate") in which the emergent degrees of freedom are intense, classical gluon fields. Such resummations make otherwise opaque features of the PDF's amenable to first-principles analysis, and they are thus ideal tools to study the rich features of spin and orbital angular momentum in a dense hadronic system. In this talk, we illustrate one such calculation, which uses an analytical resummation of QCD at high densities to dissect the quark TMD's of a heavy nucleus into individual channels that couple spin and orbital angular momentum in novel ways. This type of analysis is very generally applicable -- to a variety of processes, a variety of hadronic systems, at the quasi-classical level and after the inclusion of quantum evolution. One very robust feature of this analysis is the prediction that the presence of orbital angular momentum leads to an array of mixings among several TMD's, which allows a definitive test of the theory and, in principle, the direct extraction of the spin-orbital coupling from experiment.